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Wikispaces>Andrew_Heathwaite **Imported revision 166174095 - Original comment: ** |
Wikispaces>Andrew_Heathwaite **Imported revision 222135770 - Original comment: ** |
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<h2>IMPORTED REVISION FROM WIKISPACES</h2> | <h2>IMPORTED REVISION FROM WIKISPACES</h2> | ||
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | ||
: This revision was by author [[User:Andrew_Heathwaite|Andrew_Heathwaite]] and made on <tt> | : This revision was by author [[User:Andrew_Heathwaite|Andrew_Heathwaite]] and made on <tt>2011-04-21 15:38:24 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>222135770</tt>.<br> | ||
: The revision comment was: <tt></tt><br> | : The revision comment was: <tt></tt><br> | ||
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br> | The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br> | ||
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88cET is considered a very consonant tuning, and you will find that many of its intervals fall very close to simple ratios in 7- and 11-limit just intonation. It is also extremely close to [[41edo]], which is itself extremely close to the 8th root of 3:2 (a perfect fifth divided into exactly 8 logarithmically equal steps). See chart: | 88cET is considered a very consonant tuning, and you will find that many of its intervals fall very close to simple ratios in 7- and 11-limit just intonation. It is also extremely close to [[41edo]], which is itself extremely close to the 8th root of 3:2 (a perfect fifth divided into exactly 8 logarithmically equal steps). See chart: | ||
||~ Degree ||~ 88cET ||~ 41edo ||~ 8th Root ||~ Some Nearby || | ||~ Degree ||~ 88cET ||~ 41edo ||~ 8th Root ||~ Andrew's solfege ||~ Some Nearby || | ||
||~ ||~ ||~ 3-steps ||~ of 3:2 ||~ JI Intervals || | ||~ ||~ ||~ 3-steps ||~ of 3:2 ||~ syllable ||~ JI Intervals || | ||
|||||||||| | ||||||||||||~ **//first octave//** || | ||
|| 0 || 0 || 0 || 0 || 1/1=0 || | || 0 || 0 || 0 || 0 || do || 1/1=0 || | ||
|| 1 || 88 || 87.805 || 87.744 || 22/21=80.537, 21/20=84.467, 20/19=88.801, 19/18=93.603 || | || 1 || 88 || 87.805 || 87.744 || rih || 22/21=80.537, 21/20=84.467, 20/19=88.801, 19/18=93.603 || | ||
|| 2 || 176 || 175.610 || 175.489 || [[11_10|11/10]]=165.004, 21/19=173.268, [[10_9|10/9]]=182.404 || | || 2 || 176 || 175.610 || 175.489 || reh || [[11_10|11/10]]=165.004, 21/19=173.268, [[10_9|10/9]]=182.404 || | ||
|| 3 || 264 || 263.415 || 263.233 || [[7_6|7/6]]=266.871 || | || 3 || 264 || 263.415 || 263.233 || ma || [[7_6|7/6]]=266.871 || | ||
|| 4 || 352 || 351.220 || 350.978 || [[11_9|11/9]]= 347.408, 27/22=354.547, 16/13=359.472 || | || 4 || 352 || 351.220 || 350.978 || mu || [[11_9|11/9]]= 347.408, 27/22=354.547, 16/13=359.472 || | ||
|| 5 || 440 || 439.024 || 438.722 || 32/25=427.373, [[9_7|9/7]]=435.084, 22/17 446.363 || | || 5 || 440 || 439.024 || 438.722 || mo || 32/25=427.373, [[9_7|9/7]]=435.084, 22/17 446.363 || | ||
|| 6 || 528 || 526.829 || 526.466 || 19/14=528.687, 49/36=533.742, [[15_11|15/11]]=536.95 || | || 6 || 528 || 526.829 || 526.466 || fih || 19/14=528.687, 49/36=533.742, [[15_11|15/11]]=536.95 || | ||
|| 7 || 616 || 614.634 || 614.211 || [[10_7|10/7]]=617.488 || | || 7 || 616 || 614.634 || 614.211 || se || [[10_7|10/7]]=617.488 || | ||
|| 8 || 704 || 702.439 || 701.955 || [[3_2|3/2]]=701.955 || | || 8 || 704 || 702.439 || 701.955 || sol || [[3_2|3/2]]=701.955 || | ||
|| 9 || 792 || 790.244 || 789.699 || [[11_7|11/7]]=782.492, 30/19=790.756, 128/81=792.180, 19/12=795.558, 27/17=800.910, [[8_5|8/5]]=813.686 || | || 9 || 792 || 790.244 || 789.699 || leh || [[11_7|11/7]]=782.492, 30/19=790.756, 128/81=792.180, 19/12=795.558, 27/17=800.910, [[8_5|8/5]]=813.686 || | ||
|| 10 || 880 || 878.049 || 878.444 || [[5_3|5/3]]=884.359 || | || 10 || 880 || 878.049 || 878.444 || la || [[5_3|5/3]]=884.359 || | ||
|| 11 || 968 || 965.854 || 965.188 || [[7_4|7/4]]=968.826 || | || 11 || 968 || 965.854 || 965.188 || ta || [[7_4|7/4]]=968.826 || | ||
|| 12 || 1056 || 1053.659 || 1052.933 || [[11_6|11/6]]=1049.363, 35/19=1057.627, 24/13=1061.427 || | || 12 || 1056 || 1053.659 || 1052.933 || tu || [[11_6|11/6]]=1049.363, 35/19=1057.627, 24/13=1061.427 || | ||
|| 13 || 1144 || 1141.463 || 1140.677 || 27/14=1137.039, 31/16=1145.036 || | || 13 || 1144 || 1141.463 || 1140.677 || to || 27/14=1137.039, 31/16=1145.036 || | ||
|||||||||| | ||||||||||||~ **//second octave//** || | ||
|| 14 || 32 || 29.268 || 28.421 || 65/64=26.841, 64/63=27.264, 63/62=27.700, 58/57=30.109 || | || 14 || 32 || 29.268 || 28.421 || di || 65/64=26.841, 64/63=27.264, 63/62=27.700, 58/57=30.109 || | ||
|| 15 || 120 || 117.073 || 116.166 || 16/15=111.731, 15/14=119.443, 14/13=128.298 || | || 15 || 120 || 117.073 || 116.166 || ra || 16/15=111.731, 15/14=119.443, 14/13=128.298 || | ||
|| 16 || 208 || 204.878 || 203.910 || 9/8=203.910 || | || 16 || 208 || 204.878 || 203.910 || re || 9/8=203.910 || | ||
|| 17 || 296 || 292.683 || 291.654 || 13/11=289.210, 32/27=294.135, 19/16=297.513 || | || 17 || 296 || 292.683 || 291.654 || meh || 13/11=289.210, 32/27=294.135, 19/16=297.513 || | ||
|| 18 || 384 || 380.488 || 379.399 || 5/4=386.314 || | || 18 || 384 || 380.488 || 379.399 || mi || 5/4=386.314 || | ||
|| 19 || 472 || 468.293 || 467.143 || 17/13=464.428, 21/16=470.781 || | || 19 || 472 || 468.293 || 467.143 || fe || 17/13=464.428, 21/16=470.781 || | ||
|| 20 || 560 || 556.098 || 554.888 || 11/8=551.318, 18/13=563.382 || | || 20 || 560 || 556.098 || 554.888 || fu || 11/8=551.318, 18/13=563.382 || | ||
|| 21 || 648 || 643.902 || 642.632 || 16/11=648.682 || | || 21 || 648 || 643.902 || 642.632 || su || 16/11=648.682 || | ||
|| 22 || 736 || 731.707 || 730.376 || 32/21=729.219, 26/17=735.572, 49/32=737.652 || | || 22 || 736 || 731.707 || 730.376 || si || 32/21=729.219, 26/17=735.572, 49/32=737.652 || | ||
|| 23 || 824 || 819.512 || 818.121 || 8/5=813.686, 45/28=821.398, 21/13=830.253 || | || 23 || 824 || 819.512 || 818.121 || le || 8/5=813.686, 45/28=821.398, 21/13=830.253 || | ||
|| 24 || 912 || 907.317 || 905.865 || 42/25=898.153, 32/19=902.487, 27/16=905.865, 22/13=910.790, 17/10=918.642 || | || 24 || 912 || 907.317 || 905.865 || laa || 42/25=898.153, 32/19=902.487, 27/16=905.865, 22/13=910.790, 17/10=918.642 || | ||
|| 25 || 1000 || 995.122 || 993.609 || 39/22=991.165, 16/9=996.090, 25/14=1003.802, 34/19=1007.442 || | || 25 || 1000 || 995.122 || 993.609 || teh || 39/22=991.165, 16/9=996.090, 25/14=1003.802, 34/19=1007.442 || | ||
|| 26 || 1088 || 1082.927 || 1081.354 || 28/15=1080.557, 15/8=1088.269 || | || 26 || 1088 || 1082.927 || 1081.354 || ti || 28/15=1080.557, 15/8=1088.269 || | ||
|| 27 || 1176 || 1170.732 || 1169.098 || 63/32=1172.736, 160/81=1178.494 || | || 27 || 1176 || 1170.732 || 1169.098 || da || 63/32=1172.736, 160/81=1178.494 || | ||
|||||||||| | ||||||||||||~ **//third octave//** || | ||
|| 28 || 64 || 58.537 || 56.843 || 33/3253.273, 28/27=62.961, 80/77=66.170, 27/26=65.337 || | || 28 || 64 || 58.537 || 56.843 || ro || 33/3253.273, 28/27=62.961, 80/77=66.170, 27/26=65.337 || | ||
|| 29 || 152 || 146.341 || 144.587 || 49/45=147.428, 12/11=150.637, 35/32=155.140 || | || 29 || 152 || 146.341 || 144.587 || ru || 49/45=147.428, 12/11=150.637, 35/32=155.140 || | ||
|| 30 || 240 || 234.146 || 232.331 || 8/7=231.174, 23/20=241.961, 15/13=247.741 || | || 30 || 240 || 234.146 || 232.331 || ri || 8/7=231.174, 23/20=241.961, 15/13=247.741 || | ||
|| 31 || 328 || 321.951 || 320.076 || 6/5=315.641, 23/19=330.761 || | || 31 || 328 || 321.951 || 320.076 || me || 6/5=315.641, 23/19=330.761 || | ||
|| 32 || 416 || 409.756 || 407.820 || 81/64=407.820, 33/26=412.745, 14/11=417.508 || | || 32 || 416 || 409.756 || 407.820 || maa || 81/64=407.820, 33/26=412.745, 14/11=417.508 || | ||
|| 33 || 504 || 497.561 || 495.564 || 85/64=491.269, 4/3=498.045, 75/56=505.757 || | || 33 || 504 || 497.561 || 495.564 || fa || 85/64=491.269, 4/3=498.045, 75/56=505.757 || | ||
|| 34 || 592 || 585.366 || 583.309 || 7/5=582.512, 45/32=590.224, 38/27=591.648 || | || 34 || 592 || 585.366 || 583.309 || fi || 7/5=582.512, 45/32=590.224, 38/27=591.648 || | ||
|| 35 || 680 || 673.171 || 671.053 || 28/19=671.313, 40/27=680.449 || | || 35 || 680 || 673.171 || 671.053 || sih || 28/19=671.313, 40/27=680.449 || | ||
|| 36 || 768 || 760.976 || 758.798 || 17/11=753.637, 99/64=755.228, 14/9=764.916, 39/25=769.855, 25/16=772.627 || | || 36 || 768 || 760.976 || 758.798 || lo || 17/11=753.637, 99/64=755.228, 14/9=764.916, 39/25=769.855, 25/16=772.627 || | ||
|| 37 || 856 || 848.780 || 846.542 || 13/8=840.528, 18/11=852.592 || | || 37 || 856 || 848.780 || 846.542 || lu || 13/8=840.528, 18/11=852.592 || | ||
|| 38 || 944 || 936.585 || 934.286 || 12/7=933.129, 19/11=946.195 || | || 38 || 944 || 936.585 || 934.286 || li || 12/7=933.129, 19/11=946.195 || | ||
|| 39 || 1032 || 1024.390 || 1022.031 || 9/5=1017.596, 49/27=1031.787, 20/11=1034.996 || | || 39 || 1032 || 1024.390 || 1022.031 || te || 9/5=1017.596, 49/27=1031.787, 20/11=1034.996 || | ||
|| 40 || 1120 || 1112.195 || 1109.775 || 36/19=1106.397, 243/128=1109.775, 19/10=1111.199, 21/11=1119.463 || | || 40 || 1120 || 1112.195 || 1109.775 || taa || 36/19=1106.397, 243/128=1109.775, 19/10=1111.199, 21/11=1119.463 || | ||
|||||||||| | ||||||||||||~ **//fourth octave//** (near match) || | ||
|| 41 || 8 || 0 || 1197.59 || 1/1=0, 2/1=1200 || | || 41 || 8 || 0 || 1197.59 || do || 1/1=0, 2/1=1200 || | ||
==Compositions== | ==Compositions== | ||
| Line 100: | Line 100: | ||
</th> | </th> | ||
<th>8th Root<br /> | <th>8th Root<br /> | ||
</th> | |||
<th>Andrew's solfege<br /> | |||
</th> | </th> | ||
<th>Some Nearby<br /> | <th>Some Nearby<br /> | ||
| Line 112: | Line 114: | ||
</th> | </th> | ||
<th>of 3:2<br /> | <th>of 3:2<br /> | ||
</th> | |||
<th>syllable<br /> | |||
</th> | </th> | ||
<th>JI Intervals<br /> | <th>JI Intervals<br /> | ||
| Line 117: | Line 121: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
< | <th colspan="6"><strong><em>first octave</em></strong><br /> | ||
</ | </th> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
| Line 128: | Line 132: | ||
</td> | </td> | ||
<td>0<br /> | <td>0<br /> | ||
</td> | |||
<td>do<br /> | |||
</td> | </td> | ||
<td>1/1=0<br /> | <td>1/1=0<br /> | ||
| Line 140: | Line 146: | ||
</td> | </td> | ||
<td>87.744<br /> | <td>87.744<br /> | ||
</td> | |||
<td>rih<br /> | |||
</td> | </td> | ||
<td>22/21=80.537, 21/20=84.467, 20/19=88.801, 19/18=93.603<br /> | <td>22/21=80.537, 21/20=84.467, 20/19=88.801, 19/18=93.603<br /> | ||
| Line 152: | Line 160: | ||
</td> | </td> | ||
<td>175.489<br /> | <td>175.489<br /> | ||
</td> | |||
<td>reh<br /> | |||
</td> | </td> | ||
<td><a class="wiki_link" href="/11_10">11/10</a>=165.004, 21/19=173.268, <a class="wiki_link" href="/10_9">10/9</a>=182.404<br /> | <td><a class="wiki_link" href="/11_10">11/10</a>=165.004, 21/19=173.268, <a class="wiki_link" href="/10_9">10/9</a>=182.404<br /> | ||
| Line 164: | Line 174: | ||
</td> | </td> | ||
<td>263.233<br /> | <td>263.233<br /> | ||
</td> | |||
<td>ma<br /> | |||
</td> | </td> | ||
<td><a class="wiki_link" href="/7_6">7/6</a>=266.871<br /> | <td><a class="wiki_link" href="/7_6">7/6</a>=266.871<br /> | ||
| Line 176: | Line 188: | ||
</td> | </td> | ||
<td>350.978<br /> | <td>350.978<br /> | ||
</td> | |||
<td>mu<br /> | |||
</td> | </td> | ||
<td><a class="wiki_link" href="/11_9">11/9</a>= 347.408, 27/22=354.547, 16/13=359.472<br /> | <td><a class="wiki_link" href="/11_9">11/9</a>= 347.408, 27/22=354.547, 16/13=359.472<br /> | ||
| Line 188: | Line 202: | ||
</td> | </td> | ||
<td>438.722<br /> | <td>438.722<br /> | ||
</td> | |||
<td>mo<br /> | |||
</td> | </td> | ||
<td>32/25=427.373, <a class="wiki_link" href="/9_7">9/7</a>=435.084, 22/17 446.363<br /> | <td>32/25=427.373, <a class="wiki_link" href="/9_7">9/7</a>=435.084, 22/17 446.363<br /> | ||
| Line 200: | Line 216: | ||
</td> | </td> | ||
<td>526.466<br /> | <td>526.466<br /> | ||
</td> | |||
<td>fih<br /> | |||
</td> | </td> | ||
<td>19/14=528.687, 49/36=533.742, <a class="wiki_link" href="/15_11">15/11</a>=536.95<br /> | <td>19/14=528.687, 49/36=533.742, <a class="wiki_link" href="/15_11">15/11</a>=536.95<br /> | ||
| Line 212: | Line 230: | ||
</td> | </td> | ||
<td>614.211<br /> | <td>614.211<br /> | ||
</td> | |||
<td>se<br /> | |||
</td> | </td> | ||
<td><a class="wiki_link" href="/10_7">10/7</a>=617.488<br /> | <td><a class="wiki_link" href="/10_7">10/7</a>=617.488<br /> | ||
| Line 224: | Line 244: | ||
</td> | </td> | ||
<td>701.955<br /> | <td>701.955<br /> | ||
</td> | |||
<td>sol<br /> | |||
</td> | </td> | ||
<td><a class="wiki_link" href="/3_2">3/2</a>=701.955<br /> | <td><a class="wiki_link" href="/3_2">3/2</a>=701.955<br /> | ||
| Line 236: | Line 258: | ||
</td> | </td> | ||
<td>789.699<br /> | <td>789.699<br /> | ||
</td> | |||
<td>leh<br /> | |||
</td> | </td> | ||
<td><a class="wiki_link" href="/11_7">11/7</a>=782.492, 30/19=790.756, 128/81=792.180, 19/12=795.558, 27/17=800.910, <a class="wiki_link" href="/8_5">8/5</a>=813.686<br /> | <td><a class="wiki_link" href="/11_7">11/7</a>=782.492, 30/19=790.756, 128/81=792.180, 19/12=795.558, 27/17=800.910, <a class="wiki_link" href="/8_5">8/5</a>=813.686<br /> | ||
| Line 248: | Line 272: | ||
</td> | </td> | ||
<td>878.444<br /> | <td>878.444<br /> | ||
</td> | |||
<td>la<br /> | |||
</td> | </td> | ||
<td><a class="wiki_link" href="/5_3">5/3</a>=884.359<br /> | <td><a class="wiki_link" href="/5_3">5/3</a>=884.359<br /> | ||
| Line 260: | Line 286: | ||
</td> | </td> | ||
<td>965.188<br /> | <td>965.188<br /> | ||
</td> | |||
<td>ta<br /> | |||
</td> | </td> | ||
<td><a class="wiki_link" href="/7_4">7/4</a>=968.826<br /> | <td><a class="wiki_link" href="/7_4">7/4</a>=968.826<br /> | ||
| Line 272: | Line 300: | ||
</td> | </td> | ||
<td>1052.933<br /> | <td>1052.933<br /> | ||
</td> | |||
<td>tu<br /> | |||
</td> | </td> | ||
<td><a class="wiki_link" href="/11_6">11/6</a>=1049.363, 35/19=1057.627, 24/13=1061.427<br /> | <td><a class="wiki_link" href="/11_6">11/6</a>=1049.363, 35/19=1057.627, 24/13=1061.427<br /> | ||
| Line 284: | Line 314: | ||
</td> | </td> | ||
<td>1140.677<br /> | <td>1140.677<br /> | ||
</td> | |||
<td>to<br /> | |||
</td> | </td> | ||
<td>27/14=1137.039, 31/16=1145.036<br /> | <td>27/14=1137.039, 31/16=1145.036<br /> | ||
| Line 289: | Line 321: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
< | <th colspan="6"><strong><em>second octave</em></strong><br /> | ||
</ | </th> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
| Line 300: | Line 332: | ||
</td> | </td> | ||
<td>28.421<br /> | <td>28.421<br /> | ||
</td> | |||
<td>di<br /> | |||
</td> | </td> | ||
<td>65/64=26.841, 64/63=27.264, 63/62=27.700, 58/57=30.109<br /> | <td>65/64=26.841, 64/63=27.264, 63/62=27.700, 58/57=30.109<br /> | ||
| Line 312: | Line 346: | ||
</td> | </td> | ||
<td>116.166<br /> | <td>116.166<br /> | ||
</td> | |||
<td>ra<br /> | |||
</td> | </td> | ||
<td>16/15=111.731, 15/14=119.443, 14/13=128.298<br /> | <td>16/15=111.731, 15/14=119.443, 14/13=128.298<br /> | ||
| Line 324: | Line 360: | ||
</td> | </td> | ||
<td>203.910<br /> | <td>203.910<br /> | ||
</td> | |||
<td>re<br /> | |||
</td> | </td> | ||
<td>9/8=203.910<br /> | <td>9/8=203.910<br /> | ||
| Line 336: | Line 374: | ||
</td> | </td> | ||
<td>291.654<br /> | <td>291.654<br /> | ||
</td> | |||
<td>meh<br /> | |||
</td> | </td> | ||
<td>13/11=289.210, 32/27=294.135, 19/16=297.513<br /> | <td>13/11=289.210, 32/27=294.135, 19/16=297.513<br /> | ||
| Line 348: | Line 388: | ||
</td> | </td> | ||
<td>379.399<br /> | <td>379.399<br /> | ||
</td> | |||
<td>mi<br /> | |||
</td> | </td> | ||
<td>5/4=386.314<br /> | <td>5/4=386.314<br /> | ||
| Line 360: | Line 402: | ||
</td> | </td> | ||
<td>467.143<br /> | <td>467.143<br /> | ||
</td> | |||
<td>fe<br /> | |||
</td> | </td> | ||
<td>17/13=464.428, 21/16=470.781<br /> | <td>17/13=464.428, 21/16=470.781<br /> | ||
| Line 372: | Line 416: | ||
</td> | </td> | ||
<td>554.888<br /> | <td>554.888<br /> | ||
</td> | |||
<td>fu<br /> | |||
</td> | </td> | ||
<td>11/8=551.318, 18/13=563.382<br /> | <td>11/8=551.318, 18/13=563.382<br /> | ||
| Line 384: | Line 430: | ||
</td> | </td> | ||
<td>642.632<br /> | <td>642.632<br /> | ||
</td> | |||
<td>su<br /> | |||
</td> | </td> | ||
<td>16/11=648.682<br /> | <td>16/11=648.682<br /> | ||
| Line 396: | Line 444: | ||
</td> | </td> | ||
<td>730.376<br /> | <td>730.376<br /> | ||
</td> | |||
<td>si<br /> | |||
</td> | </td> | ||
<td>32/21=729.219, 26/17=735.572, 49/32=737.652<br /> | <td>32/21=729.219, 26/17=735.572, 49/32=737.652<br /> | ||
| Line 408: | Line 458: | ||
</td> | </td> | ||
<td>818.121<br /> | <td>818.121<br /> | ||
</td> | |||
<td>le<br /> | |||
</td> | </td> | ||
<td>8/5=813.686, 45/28=821.398, 21/13=830.253<br /> | <td>8/5=813.686, 45/28=821.398, 21/13=830.253<br /> | ||
| Line 420: | Line 472: | ||
</td> | </td> | ||
<td>905.865<br /> | <td>905.865<br /> | ||
</td> | |||
<td>laa<br /> | |||
</td> | </td> | ||
<td>42/25=898.153, 32/19=902.487, 27/16=905.865, 22/13=910.790, 17/10=918.642<br /> | <td>42/25=898.153, 32/19=902.487, 27/16=905.865, 22/13=910.790, 17/10=918.642<br /> | ||
| Line 432: | Line 486: | ||
</td> | </td> | ||
<td>993.609<br /> | <td>993.609<br /> | ||
</td> | |||
<td>teh<br /> | |||
</td> | </td> | ||
<td>39/22=991.165, 16/9=996.090, 25/14=1003.802, 34/19=1007.442<br /> | <td>39/22=991.165, 16/9=996.090, 25/14=1003.802, 34/19=1007.442<br /> | ||
| Line 444: | Line 500: | ||
</td> | </td> | ||
<td>1081.354<br /> | <td>1081.354<br /> | ||
</td> | |||
<td>ti<br /> | |||
</td> | </td> | ||
<td>28/15=1080.557, 15/8=1088.269<br /> | <td>28/15=1080.557, 15/8=1088.269<br /> | ||
| Line 456: | Line 514: | ||
</td> | </td> | ||
<td>1169.098<br /> | <td>1169.098<br /> | ||
</td> | |||
<td>da<br /> | |||
</td> | </td> | ||
<td>63/32=1172.736, 160/81=1178.494<br /> | <td>63/32=1172.736, 160/81=1178.494<br /> | ||
| Line 461: | Line 521: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
< | <th colspan="6"><strong><em>third octave</em></strong><br /> | ||
</ | </th> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
| Line 472: | Line 532: | ||
</td> | </td> | ||
<td>56.843<br /> | <td>56.843<br /> | ||
</td> | |||
<td>ro<br /> | |||
</td> | </td> | ||
<td>33/3253.273, 28/27=62.961, 80/77=66.170, 27/26=65.337<br /> | <td>33/3253.273, 28/27=62.961, 80/77=66.170, 27/26=65.337<br /> | ||
| Line 484: | Line 546: | ||
</td> | </td> | ||
<td>144.587<br /> | <td>144.587<br /> | ||
</td> | |||
<td>ru<br /> | |||
</td> | </td> | ||
<td>49/45=147.428, 12/11=150.637, 35/32=155.140<br /> | <td>49/45=147.428, 12/11=150.637, 35/32=155.140<br /> | ||
| Line 496: | Line 560: | ||
</td> | </td> | ||
<td>232.331<br /> | <td>232.331<br /> | ||
</td> | |||
<td>ri<br /> | |||
</td> | </td> | ||
<td>8/7=231.174, 23/20=241.961, 15/13=247.741<br /> | <td>8/7=231.174, 23/20=241.961, 15/13=247.741<br /> | ||
| Line 508: | Line 574: | ||
</td> | </td> | ||
<td>320.076<br /> | <td>320.076<br /> | ||
</td> | |||
<td>me<br /> | |||
</td> | </td> | ||
<td>6/5=315.641, 23/19=330.761<br /> | <td>6/5=315.641, 23/19=330.761<br /> | ||
| Line 520: | Line 588: | ||
</td> | </td> | ||
<td>407.820<br /> | <td>407.820<br /> | ||
</td> | |||
<td>maa<br /> | |||
</td> | </td> | ||
<td>81/64=407.820, 33/26=412.745, 14/11=417.508<br /> | <td>81/64=407.820, 33/26=412.745, 14/11=417.508<br /> | ||
| Line 532: | Line 602: | ||
</td> | </td> | ||
<td>495.564<br /> | <td>495.564<br /> | ||
</td> | |||
<td>fa<br /> | |||
</td> | </td> | ||
<td>85/64=491.269, 4/3=498.045, 75/56=505.757<br /> | <td>85/64=491.269, 4/3=498.045, 75/56=505.757<br /> | ||
| Line 544: | Line 616: | ||
</td> | </td> | ||
<td>583.309<br /> | <td>583.309<br /> | ||
</td> | |||
<td>fi<br /> | |||
</td> | </td> | ||
<td>7/5=582.512, 45/32=590.224, 38/27=591.648<br /> | <td>7/5=582.512, 45/32=590.224, 38/27=591.648<br /> | ||
| Line 556: | Line 630: | ||
</td> | </td> | ||
<td>671.053<br /> | <td>671.053<br /> | ||
</td> | |||
<td>sih<br /> | |||
</td> | </td> | ||
<td>28/19=671.313, 40/27=680.449<br /> | <td>28/19=671.313, 40/27=680.449<br /> | ||
| Line 568: | Line 644: | ||
</td> | </td> | ||
<td>758.798<br /> | <td>758.798<br /> | ||
</td> | |||
<td>lo<br /> | |||
</td> | </td> | ||
<td>17/11=753.637, 99/64=755.228, 14/9=764.916, 39/25=769.855, 25/16=772.627<br /> | <td>17/11=753.637, 99/64=755.228, 14/9=764.916, 39/25=769.855, 25/16=772.627<br /> | ||
| Line 580: | Line 658: | ||
</td> | </td> | ||
<td>846.542<br /> | <td>846.542<br /> | ||
</td> | |||
<td>lu<br /> | |||
</td> | </td> | ||
<td>13/8=840.528, 18/11=852.592<br /> | <td>13/8=840.528, 18/11=852.592<br /> | ||
| Line 592: | Line 672: | ||
</td> | </td> | ||
<td>934.286<br /> | <td>934.286<br /> | ||
</td> | |||
<td>li<br /> | |||
</td> | </td> | ||
<td>12/7=933.129, 19/11=946.195<br /> | <td>12/7=933.129, 19/11=946.195<br /> | ||
| Line 604: | Line 686: | ||
</td> | </td> | ||
<td>1022.031<br /> | <td>1022.031<br /> | ||
</td> | |||
<td>te<br /> | |||
</td> | </td> | ||
<td>9/5=1017.596, 49/27=1031.787, 20/11=1034.996<br /> | <td>9/5=1017.596, 49/27=1031.787, 20/11=1034.996<br /> | ||
| Line 616: | Line 700: | ||
</td> | </td> | ||
<td>1109.775<br /> | <td>1109.775<br /> | ||
</td> | |||
<td>taa<br /> | |||
</td> | </td> | ||
<td>36/19=1106.397, 243/128=1109.775, 19/10=1111.199, 21/11=1119.463<br /> | <td>36/19=1106.397, 243/128=1109.775, 19/10=1111.199, 21/11=1119.463<br /> | ||
| Line 621: | Line 707: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
< | <th colspan="6"><strong><em>fourth octave</em></strong> (near match)<br /> | ||
</ | </th> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
| Line 632: | Line 718: | ||
</td> | </td> | ||
<td>1197.59<br /> | <td>1197.59<br /> | ||
</td> | |||
<td>do<br /> | |||
</td> | </td> | ||
<td>1/1=0, 2/1=1200<br /> | <td>1/1=0, 2/1=1200<br /> | ||
Revision as of 15:38, 21 April 2011
IMPORTED REVISION FROM WIKISPACES
This is an imported revision from Wikispaces. The revision metadata is included below for reference:
- This revision was by author Andrew_Heathwaite and made on 2011-04-21 15:38:24 UTC.
- The original revision id was 222135770.
- The revision comment was:
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.
Original Wikitext content:
=88cET= ==Theory== 88 cent equal temperament uses 88 cents, or 11/150 of an octave, to generate a nonoctave rank one scale. Since 88 cents is an excellent generator for [[Tetracot family|octacot temperament]], it can be viewed as the generator chain of octacot, stripped of octaves. However viewed, octacot and 88 cents equal temperament are very closely related. Eight steps of 88 cents gives 704 cents, two cents sharp of 3/2, and eighteen gives 1584 cents, two cents flat of 5/2. Taken together this tells us that (5/2)^4/(3/2)^9 = 20000/19683, the minimal diesis or tetracot comma, must be being tempered out. Eleven steps of 88 cents gives 968 cents, less than a cent flat of 7/4, and this tells us that (7/4)^8/(3/2)^11 = 5764801/5668704 must be tempered out also. Taking this, multiplying it by the tetracot comma and taking the fourth root yields 245/243, which therefore must be tempered out also. The tetracot comma and 245/243 taken together define 7-limit octacot. Continuing on, twenty steps of 88 cents gives 1760 cents, whioh we may compare to the 1751.3 cents of 11/4 and suggests 100/99 being tempered out, and four steps gives 352 cents, which may be compared to the 359.5 cents of 16/13, and suggestes 325/324 being tempered out. These would give an extended octacot, for which 88 cents would be an excellent generator tuning. ==Intervals== 88cET is considered a very consonant tuning, and you will find that many of its intervals fall very close to simple ratios in 7- and 11-limit just intonation. It is also extremely close to [[41edo]], which is itself extremely close to the 8th root of 3:2 (a perfect fifth divided into exactly 8 logarithmically equal steps). See chart: ||~ Degree ||~ 88cET ||~ 41edo ||~ 8th Root ||~ Andrew's solfege ||~ Some Nearby || ||~ ||~ ||~ 3-steps ||~ of 3:2 ||~ syllable ||~ JI Intervals || ||||||||||||~ **//first octave//** || || 0 || 0 || 0 || 0 || do || 1/1=0 || || 1 || 88 || 87.805 || 87.744 || rih || 22/21=80.537, 21/20=84.467, 20/19=88.801, 19/18=93.603 || || 2 || 176 || 175.610 || 175.489 || reh || [[11_10|11/10]]=165.004, 21/19=173.268, [[10_9|10/9]]=182.404 || || 3 || 264 || 263.415 || 263.233 || ma || [[7_6|7/6]]=266.871 || || 4 || 352 || 351.220 || 350.978 || mu || [[11_9|11/9]]= 347.408, 27/22=354.547, 16/13=359.472 || || 5 || 440 || 439.024 || 438.722 || mo || 32/25=427.373, [[9_7|9/7]]=435.084, 22/17 446.363 || || 6 || 528 || 526.829 || 526.466 || fih || 19/14=528.687, 49/36=533.742, [[15_11|15/11]]=536.95 || || 7 || 616 || 614.634 || 614.211 || se || [[10_7|10/7]]=617.488 || || 8 || 704 || 702.439 || 701.955 || sol || [[3_2|3/2]]=701.955 || || 9 || 792 || 790.244 || 789.699 || leh || [[11_7|11/7]]=782.492, 30/19=790.756, 128/81=792.180, 19/12=795.558, 27/17=800.910, [[8_5|8/5]]=813.686 || || 10 || 880 || 878.049 || 878.444 || la || [[5_3|5/3]]=884.359 || || 11 || 968 || 965.854 || 965.188 || ta || [[7_4|7/4]]=968.826 || || 12 || 1056 || 1053.659 || 1052.933 || tu || [[11_6|11/6]]=1049.363, 35/19=1057.627, 24/13=1061.427 || || 13 || 1144 || 1141.463 || 1140.677 || to || 27/14=1137.039, 31/16=1145.036 || ||||||||||||~ **//second octave//** || || 14 || 32 || 29.268 || 28.421 || di || 65/64=26.841, 64/63=27.264, 63/62=27.700, 58/57=30.109 || || 15 || 120 || 117.073 || 116.166 || ra || 16/15=111.731, 15/14=119.443, 14/13=128.298 || || 16 || 208 || 204.878 || 203.910 || re || 9/8=203.910 || || 17 || 296 || 292.683 || 291.654 || meh || 13/11=289.210, 32/27=294.135, 19/16=297.513 || || 18 || 384 || 380.488 || 379.399 || mi || 5/4=386.314 || || 19 || 472 || 468.293 || 467.143 || fe || 17/13=464.428, 21/16=470.781 || || 20 || 560 || 556.098 || 554.888 || fu || 11/8=551.318, 18/13=563.382 || || 21 || 648 || 643.902 || 642.632 || su || 16/11=648.682 || || 22 || 736 || 731.707 || 730.376 || si || 32/21=729.219, 26/17=735.572, 49/32=737.652 || || 23 || 824 || 819.512 || 818.121 || le || 8/5=813.686, 45/28=821.398, 21/13=830.253 || || 24 || 912 || 907.317 || 905.865 || laa || 42/25=898.153, 32/19=902.487, 27/16=905.865, 22/13=910.790, 17/10=918.642 || || 25 || 1000 || 995.122 || 993.609 || teh || 39/22=991.165, 16/9=996.090, 25/14=1003.802, 34/19=1007.442 || || 26 || 1088 || 1082.927 || 1081.354 || ti || 28/15=1080.557, 15/8=1088.269 || || 27 || 1176 || 1170.732 || 1169.098 || da || 63/32=1172.736, 160/81=1178.494 || ||||||||||||~ **//third octave//** || || 28 || 64 || 58.537 || 56.843 || ro || 33/3253.273, 28/27=62.961, 80/77=66.170, 27/26=65.337 || || 29 || 152 || 146.341 || 144.587 || ru || 49/45=147.428, 12/11=150.637, 35/32=155.140 || || 30 || 240 || 234.146 || 232.331 || ri || 8/7=231.174, 23/20=241.961, 15/13=247.741 || || 31 || 328 || 321.951 || 320.076 || me || 6/5=315.641, 23/19=330.761 || || 32 || 416 || 409.756 || 407.820 || maa || 81/64=407.820, 33/26=412.745, 14/11=417.508 || || 33 || 504 || 497.561 || 495.564 || fa || 85/64=491.269, 4/3=498.045, 75/56=505.757 || || 34 || 592 || 585.366 || 583.309 || fi || 7/5=582.512, 45/32=590.224, 38/27=591.648 || || 35 || 680 || 673.171 || 671.053 || sih || 28/19=671.313, 40/27=680.449 || || 36 || 768 || 760.976 || 758.798 || lo || 17/11=753.637, 99/64=755.228, 14/9=764.916, 39/25=769.855, 25/16=772.627 || || 37 || 856 || 848.780 || 846.542 || lu || 13/8=840.528, 18/11=852.592 || || 38 || 944 || 936.585 || 934.286 || li || 12/7=933.129, 19/11=946.195 || || 39 || 1032 || 1024.390 || 1022.031 || te || 9/5=1017.596, 49/27=1031.787, 20/11=1034.996 || || 40 || 1120 || 1112.195 || 1109.775 || taa || 36/19=1106.397, 243/128=1109.775, 19/10=1111.199, 21/11=1119.463 || ||||||||||||~ **//fourth octave//** (near match) || || 41 || 8 || 0 || 1197.59 || do || 1/1=0, 2/1=1200 || ==Compositions== [[http://www.seraph.it/dep/det/88east.mp3|88 East]] by [[Carlo Serafini]] [[http://www.seraph.it/dep/det/88vocoeast.mp3|88 VocoEast]] by [[Carlo Serafini]] [[http://www.seraph.it/dep/det/88Bulgarians.mp3|88 Bulgarians]] by [[Carlo Serafini]] ([[http://www.seraph.it/blog_files/9660ca3450a996ea8b55713cbf36151f-15.html|blog entry]]) [[http://www.seraph.it/dep/int/88jinglebells.mp3|88 Jingle Bells]] by [[Carlo Serafini]] ([[http://www.seraph.it/blog_files/495ec175ce56cf38cb399d1cd24db164-17.html|blog entry]])
Original HTML content:
<html><head><title>88cET</title></head><body><!-- ws:start:WikiTextHeadingRule:0:<h1> --><h1 id="toc0"><a name="x88cET"></a><!-- ws:end:WikiTextHeadingRule:0 -->88cET</h1>
<br />
<!-- ws:start:WikiTextHeadingRule:2:<h2> --><h2 id="toc1"><a name="x88cET-Theory"></a><!-- ws:end:WikiTextHeadingRule:2 -->Theory</h2>
<br />
88 cent equal temperament uses 88 cents, or 11/150 of an octave, to generate a nonoctave rank one scale. Since 88 cents is an excellent generator for <a class="wiki_link" href="/Tetracot%20family">octacot temperament</a>, it can be viewed as the generator chain of octacot, stripped of octaves. However viewed, octacot and 88 cents equal temperament are very closely related.<br />
<br />
Eight steps of 88 cents gives 704 cents, two cents sharp of 3/2, and eighteen gives 1584 cents, two cents flat of 5/2. Taken together this tells us that (5/2)^4/(3/2)^9 = 20000/19683, the minimal diesis or tetracot comma, must be being tempered out. Eleven steps of 88 cents gives 968 cents, less than a cent flat of 7/4, and this tells us that (7/4)^8/(3/2)^11 = 5764801/5668704 must be tempered out also. Taking this, multiplying it by the tetracot comma and taking the fourth root yields 245/243, which therefore must be tempered out also. The tetracot comma and 245/243 taken together define 7-limit octacot. <br />
<br />
Continuing on, twenty steps of 88 cents gives 1760 cents, whioh we may compare to the 1751.3 cents of 11/4 and suggests 100/99 being tempered out, and four steps gives 352 cents, which may be compared to the 359.5 cents of 16/13, and suggestes 325/324 being tempered out. These would give an extended octacot, for which 88 cents would be an excellent generator tuning.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:4:<h2> --><h2 id="toc2"><a name="x88cET-Intervals"></a><!-- ws:end:WikiTextHeadingRule:4 -->Intervals</h2>
<br />
88cET is considered a very consonant tuning, and you will find that many of its intervals fall very close to simple ratios in 7- and 11-limit just intonation. It is also extremely close to <a class="wiki_link" href="/41edo">41edo</a>, which is itself extremely close to the 8th root of 3:2 (a perfect fifth divided into exactly 8 logarithmically equal steps). See chart:<br />
<br />
<table class="wiki_table">
<tr>
<th>Degree<br />
</th>
<th>88cET<br />
</th>
<th>41edo<br />
</th>
<th>8th Root<br />
</th>
<th>Andrew's solfege<br />
</th>
<th>Some Nearby<br />
</th>
</tr>
<tr>
<th><br />
</th>
<th><br />
</th>
<th>3-steps<br />
</th>
<th>of 3:2<br />
</th>
<th>syllable<br />
</th>
<th>JI Intervals<br />
</th>
</tr>
<tr>
<th colspan="6"><strong><em>first octave</em></strong><br />
</th>
</tr>
<tr>
<td>0<br />
</td>
<td>0<br />
</td>
<td>0<br />
</td>
<td>0<br />
</td>
<td>do<br />
</td>
<td>1/1=0<br />
</td>
</tr>
<tr>
<td>1<br />
</td>
<td>88<br />
</td>
<td>87.805<br />
</td>
<td>87.744<br />
</td>
<td>rih<br />
</td>
<td>22/21=80.537, 21/20=84.467, 20/19=88.801, 19/18=93.603<br />
</td>
</tr>
<tr>
<td>2<br />
</td>
<td>176<br />
</td>
<td>175.610<br />
</td>
<td>175.489<br />
</td>
<td>reh<br />
</td>
<td><a class="wiki_link" href="/11_10">11/10</a>=165.004, 21/19=173.268, <a class="wiki_link" href="/10_9">10/9</a>=182.404<br />
</td>
</tr>
<tr>
<td>3<br />
</td>
<td>264<br />
</td>
<td>263.415<br />
</td>
<td>263.233<br />
</td>
<td>ma<br />
</td>
<td><a class="wiki_link" href="/7_6">7/6</a>=266.871<br />
</td>
</tr>
<tr>
<td>4<br />
</td>
<td>352<br />
</td>
<td>351.220<br />
</td>
<td>350.978<br />
</td>
<td>mu<br />
</td>
<td><a class="wiki_link" href="/11_9">11/9</a>= 347.408, 27/22=354.547, 16/13=359.472<br />
</td>
</tr>
<tr>
<td>5<br />
</td>
<td>440<br />
</td>
<td>439.024<br />
</td>
<td>438.722<br />
</td>
<td>mo<br />
</td>
<td>32/25=427.373, <a class="wiki_link" href="/9_7">9/7</a>=435.084, 22/17 446.363<br />
</td>
</tr>
<tr>
<td>6<br />
</td>
<td>528<br />
</td>
<td>526.829<br />
</td>
<td>526.466<br />
</td>
<td>fih<br />
</td>
<td>19/14=528.687, 49/36=533.742, <a class="wiki_link" href="/15_11">15/11</a>=536.95<br />
</td>
</tr>
<tr>
<td>7<br />
</td>
<td>616<br />
</td>
<td>614.634<br />
</td>
<td>614.211<br />
</td>
<td>se<br />
</td>
<td><a class="wiki_link" href="/10_7">10/7</a>=617.488<br />
</td>
</tr>
<tr>
<td>8<br />
</td>
<td>704<br />
</td>
<td>702.439<br />
</td>
<td>701.955<br />
</td>
<td>sol<br />
</td>
<td><a class="wiki_link" href="/3_2">3/2</a>=701.955<br />
</td>
</tr>
<tr>
<td>9<br />
</td>
<td>792<br />
</td>
<td>790.244<br />
</td>
<td>789.699<br />
</td>
<td>leh<br />
</td>
<td><a class="wiki_link" href="/11_7">11/7</a>=782.492, 30/19=790.756, 128/81=792.180, 19/12=795.558, 27/17=800.910, <a class="wiki_link" href="/8_5">8/5</a>=813.686<br />
</td>
</tr>
<tr>
<td>10<br />
</td>
<td>880<br />
</td>
<td>878.049<br />
</td>
<td>878.444<br />
</td>
<td>la<br />
</td>
<td><a class="wiki_link" href="/5_3">5/3</a>=884.359<br />
</td>
</tr>
<tr>
<td>11<br />
</td>
<td>968<br />
</td>
<td>965.854<br />
</td>
<td>965.188<br />
</td>
<td>ta<br />
</td>
<td><a class="wiki_link" href="/7_4">7/4</a>=968.826<br />
</td>
</tr>
<tr>
<td>12<br />
</td>
<td>1056<br />
</td>
<td>1053.659<br />
</td>
<td>1052.933<br />
</td>
<td>tu<br />
</td>
<td><a class="wiki_link" href="/11_6">11/6</a>=1049.363, 35/19=1057.627, 24/13=1061.427<br />
</td>
</tr>
<tr>
<td>13<br />
</td>
<td>1144<br />
</td>
<td>1141.463<br />
</td>
<td>1140.677<br />
</td>
<td>to<br />
</td>
<td>27/14=1137.039, 31/16=1145.036<br />
</td>
</tr>
<tr>
<th colspan="6"><strong><em>second octave</em></strong><br />
</th>
</tr>
<tr>
<td>14<br />
</td>
<td>32<br />
</td>
<td>29.268<br />
</td>
<td>28.421<br />
</td>
<td>di<br />
</td>
<td>65/64=26.841, 64/63=27.264, 63/62=27.700, 58/57=30.109<br />
</td>
</tr>
<tr>
<td>15<br />
</td>
<td>120<br />
</td>
<td>117.073<br />
</td>
<td>116.166<br />
</td>
<td>ra<br />
</td>
<td>16/15=111.731, 15/14=119.443, 14/13=128.298<br />
</td>
</tr>
<tr>
<td>16<br />
</td>
<td>208<br />
</td>
<td>204.878<br />
</td>
<td>203.910<br />
</td>
<td>re<br />
</td>
<td>9/8=203.910<br />
</td>
</tr>
<tr>
<td>17<br />
</td>
<td>296<br />
</td>
<td>292.683<br />
</td>
<td>291.654<br />
</td>
<td>meh<br />
</td>
<td>13/11=289.210, 32/27=294.135, 19/16=297.513<br />
</td>
</tr>
<tr>
<td>18<br />
</td>
<td>384<br />
</td>
<td>380.488<br />
</td>
<td>379.399<br />
</td>
<td>mi<br />
</td>
<td>5/4=386.314<br />
</td>
</tr>
<tr>
<td>19<br />
</td>
<td>472<br />
</td>
<td>468.293<br />
</td>
<td>467.143<br />
</td>
<td>fe<br />
</td>
<td>17/13=464.428, 21/16=470.781<br />
</td>
</tr>
<tr>
<td>20<br />
</td>
<td>560<br />
</td>
<td>556.098<br />
</td>
<td>554.888<br />
</td>
<td>fu<br />
</td>
<td>11/8=551.318, 18/13=563.382<br />
</td>
</tr>
<tr>
<td>21<br />
</td>
<td>648<br />
</td>
<td>643.902<br />
</td>
<td>642.632<br />
</td>
<td>su<br />
</td>
<td>16/11=648.682<br />
</td>
</tr>
<tr>
<td>22<br />
</td>
<td>736<br />
</td>
<td>731.707<br />
</td>
<td>730.376<br />
</td>
<td>si<br />
</td>
<td>32/21=729.219, 26/17=735.572, 49/32=737.652<br />
</td>
</tr>
<tr>
<td>23<br />
</td>
<td>824<br />
</td>
<td>819.512<br />
</td>
<td>818.121<br />
</td>
<td>le<br />
</td>
<td>8/5=813.686, 45/28=821.398, 21/13=830.253<br />
</td>
</tr>
<tr>
<td>24<br />
</td>
<td>912<br />
</td>
<td>907.317<br />
</td>
<td>905.865<br />
</td>
<td>laa<br />
</td>
<td>42/25=898.153, 32/19=902.487, 27/16=905.865, 22/13=910.790, 17/10=918.642<br />
</td>
</tr>
<tr>
<td>25<br />
</td>
<td>1000<br />
</td>
<td>995.122<br />
</td>
<td>993.609<br />
</td>
<td>teh<br />
</td>
<td>39/22=991.165, 16/9=996.090, 25/14=1003.802, 34/19=1007.442<br />
</td>
</tr>
<tr>
<td>26<br />
</td>
<td>1088<br />
</td>
<td>1082.927<br />
</td>
<td>1081.354<br />
</td>
<td>ti<br />
</td>
<td>28/15=1080.557, 15/8=1088.269<br />
</td>
</tr>
<tr>
<td>27<br />
</td>
<td>1176<br />
</td>
<td>1170.732<br />
</td>
<td>1169.098<br />
</td>
<td>da<br />
</td>
<td>63/32=1172.736, 160/81=1178.494<br />
</td>
</tr>
<tr>
<th colspan="6"><strong><em>third octave</em></strong><br />
</th>
</tr>
<tr>
<td>28<br />
</td>
<td>64<br />
</td>
<td>58.537<br />
</td>
<td>56.843<br />
</td>
<td>ro<br />
</td>
<td>33/3253.273, 28/27=62.961, 80/77=66.170, 27/26=65.337<br />
</td>
</tr>
<tr>
<td>29<br />
</td>
<td>152<br />
</td>
<td>146.341<br />
</td>
<td>144.587<br />
</td>
<td>ru<br />
</td>
<td>49/45=147.428, 12/11=150.637, 35/32=155.140<br />
</td>
</tr>
<tr>
<td>30<br />
</td>
<td>240<br />
</td>
<td>234.146<br />
</td>
<td>232.331<br />
</td>
<td>ri<br />
</td>
<td>8/7=231.174, 23/20=241.961, 15/13=247.741<br />
</td>
</tr>
<tr>
<td>31<br />
</td>
<td>328<br />
</td>
<td>321.951<br />
</td>
<td>320.076<br />
</td>
<td>me<br />
</td>
<td>6/5=315.641, 23/19=330.761<br />
</td>
</tr>
<tr>
<td>32<br />
</td>
<td>416<br />
</td>
<td>409.756<br />
</td>
<td>407.820<br />
</td>
<td>maa<br />
</td>
<td>81/64=407.820, 33/26=412.745, 14/11=417.508<br />
</td>
</tr>
<tr>
<td>33<br />
</td>
<td>504<br />
</td>
<td>497.561<br />
</td>
<td>495.564<br />
</td>
<td>fa<br />
</td>
<td>85/64=491.269, 4/3=498.045, 75/56=505.757<br />
</td>
</tr>
<tr>
<td>34<br />
</td>
<td>592<br />
</td>
<td>585.366<br />
</td>
<td>583.309<br />
</td>
<td>fi<br />
</td>
<td>7/5=582.512, 45/32=590.224, 38/27=591.648<br />
</td>
</tr>
<tr>
<td>35<br />
</td>
<td>680<br />
</td>
<td>673.171<br />
</td>
<td>671.053<br />
</td>
<td>sih<br />
</td>
<td>28/19=671.313, 40/27=680.449<br />
</td>
</tr>
<tr>
<td>36<br />
</td>
<td>768<br />
</td>
<td>760.976<br />
</td>
<td>758.798<br />
</td>
<td>lo<br />
</td>
<td>17/11=753.637, 99/64=755.228, 14/9=764.916, 39/25=769.855, 25/16=772.627<br />
</td>
</tr>
<tr>
<td>37<br />
</td>
<td>856<br />
</td>
<td>848.780<br />
</td>
<td>846.542<br />
</td>
<td>lu<br />
</td>
<td>13/8=840.528, 18/11=852.592<br />
</td>
</tr>
<tr>
<td>38<br />
</td>
<td>944<br />
</td>
<td>936.585<br />
</td>
<td>934.286<br />
</td>
<td>li<br />
</td>
<td>12/7=933.129, 19/11=946.195<br />
</td>
</tr>
<tr>
<td>39<br />
</td>
<td>1032<br />
</td>
<td>1024.390<br />
</td>
<td>1022.031<br />
</td>
<td>te<br />
</td>
<td>9/5=1017.596, 49/27=1031.787, 20/11=1034.996<br />
</td>
</tr>
<tr>
<td>40<br />
</td>
<td>1120<br />
</td>
<td>1112.195<br />
</td>
<td>1109.775<br />
</td>
<td>taa<br />
</td>
<td>36/19=1106.397, 243/128=1109.775, 19/10=1111.199, 21/11=1119.463<br />
</td>
</tr>
<tr>
<th colspan="6"><strong><em>fourth octave</em></strong> (near match)<br />
</th>
</tr>
<tr>
<td>41<br />
</td>
<td>8<br />
</td>
<td>0<br />
</td>
<td>1197.59<br />
</td>
<td>do<br />
</td>
<td>1/1=0, 2/1=1200<br />
</td>
</tr>
</table>
<br />
<!-- ws:start:WikiTextHeadingRule:6:<h2> --><h2 id="toc3"><a name="x88cET-Compositions"></a><!-- ws:end:WikiTextHeadingRule:6 -->Compositions</h2>
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